ICPC North America Qualifier 2016, Problem G
A factorial ~n!~ of a positive integer ~n~ is defined as the product of all positive integers smaller than or equal to ~n~. For example, $$\displaystyle 21! = 1 \cdot 2 \cdot 3 \cdot \dots \cdot 21 = 51\,090\,942\,171\,709\,440\,000$$
It is straightforward to calculate the factorial of a small integer, and you have probably done it many times before. In this problem, however, your task is reversed. You are given the value of ~n!~ and you have to find the value of ~n~.
The input contains the factorial ~n!~ of a positive integer ~n~. The number of digits of ~n!~ is at most ~10^6~.
Output the value of ~n~.
Sample Input 1
Sample Output 1
Sample Input 2
Sample Output 2
Sample Input 3
Sample Output 3